Title :
Gabor transform with undersampling
Author_Institution :
Dept. of Math., Connecticut Univ., Storrs, CT, USA
Abstract :
We investigate discrete Gabor transforms with undersampling. For an undersampled Gabor triple (g,a,b) (i.e.,a.b>N), we show that the associated generalized dual Gabor wavelet is the same as the one associated to (g,b˜,a˜), except for the redundancy constant factor. Then we are able to determine the best approximations, by linear combinations of Gabor elementary functions, of signals
Keywords :
approximation theory; signal representation; signal sampling; time-frequency analysis; wavelet transforms; Gabor elementary functions; approximations; discrete Gabor transforms; frequency shifts; generalized dual Gabor wavelet; linear combinations; redundancy constant factor; signal representation; time shifts; undersampled Gabor triple; undersampling; Discrete transforms; Frequency; Lattices; Linear approximation; Mathematics; Sampling methods; Signal analysis;
Conference_Titel :
Time-Frequency and Time-Scale Analysis, 1996., Proceedings of the IEEE-SP International Symposium on
Conference_Location :
Paris
Print_ISBN :
0-7803-3512-0
DOI :
10.1109/TFSA.1996.547477
